Question

Write the equation of the directrix of the parabola x² − 4x − 8y + 12 = 0.

Answer 1

Given:
x² − 4x − 8y + 12 = 0
$$\begin{gathered} \Rightarrow {\left(x-2\right)}^2-4-8y+12=0 \\ \Rightarrow {\left(x-2\right)}^2=8\left(y-1\right)\left(1\right) \end{gathered}$$

Let Y = y−1, $X=x-2$

∴ From (1), we have:

$X^2=8Y$ (2)

Comparing with $x^2=4ay$:
$a=2$

Directrix = Y = −a

⇒ y − 1 = −a

⇒y = −a + 1
= −2 + 1
= −1

Therefore, the required equation of the directrix is $y=-1$.